Spurs have been plunged into crisis this season after winning only three of their first 11 games and a horror week saw them follow up a 7-2 hammering by Bayern Munich in the Champions League with a 3-0 loss at Brighton on Saturday.
Pochettino - who guided the club to the Champions League final only five months ago - has had to defend his position, insisting he does not fear the sack.
There are clearly issues at the club, starting with a squad that needs refreshing, but Winks insists the players are still playing for Pochettino.
"He's our manager. He's been fantastic ever since he's been at the club and taken the club to new heights," Winks said. "At the moment we are going through a bit of a rough patch that happens in football. Every club goes through it."
The defeat at the Amex Stadium summed up Spurs' run of form at the moment after an error from Hugo Lloris handed Neal Maupay a simple close-range header after just three minutes.
The France international suffered a dislocated elbow as he landed after dropping the ball into Maupay's path which will sideline him for the foreseeable future.
Aaron Connolly doubled Brighton's lead on his first Premier League start, before adding a third on 65 minutes to secure his side their first win since the opening day of the season.
Winks came on at half-time but could not affect the result and apologised to the club's fans, while vowing that the players will look to put things right in training and the next match.
Spurs have the international break to reflect on their poor form before they face bottom side Watford at home on October 19.